Cremona's table of elliptic curves

552 = 2³ · 3 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 23-	Signs for the Atkin-Lehner involutions
Class	552d	Isogeny class
Conductor	552	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-12516498432 = -1 · 210 · 312 · 23	Discriminant
Eigenvalues	2- 3+  2 -4 -4 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,248,-5252]	[a1,a2,a3,a4,a6]
Generators	[38:240:1]	Generators of the group modulo torsion
j	1640689628/12223143	j-invariant
L	1.8063895255896	L(r)(E,1)/r!
Ω	0.62907516356088	Real period
R	2.8715003074745	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1104c4 4416n4 1656a4 13800l4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 552d4

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	2	-4	-4	-2	-2	0	-	-2	0	-10	-6	8	-8	-6	-4	14	8	-8	-6	12	-12	-2	10

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Quadratic twists for elliptic curve 552d4

-4	8	-3	5	-7	-11	13	-23
1104c4	4416n4	1656a4	13800l4	27048v3	66792i3	93288g3	12696o4

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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